Second order cone programming relaxation of a positive semidefinite constraint

Sunyoung Kim, Masakazu Kojima, Makoto Yamashita

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways of expressing the positive semidefinite constraint of the SDP relaxation. We present how such SOCP relaxations can be derived, and show the relationship between the resulting SOCP relaxations.

Original languageEnglish
Pages (from-to)535-541
Number of pages7
JournalOptimization Methods and Software
Issue number5
StatePublished - Oct 2003


  • Convex relaxation
  • Nonconvex program
  • Quadratic program
  • Second order cone program
  • Semidefinite program


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